A theoretical and experimental study of a new algorithm for minimum cost flow in dynamic graphs

Abstract This work focuses on the minimum cost flow problem in dynamic graphs. The model here proposed does not have travel time nor storage but all other parameters are time-dependent. The most popular method to solve this kind of problem uses the time-expanded graph but due to the large size of this graph, this solution technique is not manageable on a long time horizon. We propose a new approach that does not use the time-expanded graph. Our algorithm is based on the computation of successive shortest paths on static graphs, which are much smaller compared to the time-expanded graph. It has a significantly better computational complexity. Our method was implemented using the GraphStream library and experiments showed that it is also much faster than the classical method in practice.